W. Ferret — Law of Thermal Radiation. 9 



The great differences in the values of m above as obtained 

 from the two different forms of expression of the law of radia- 

 tion arises from the uncertainty in the values of A upon which 

 they depend. This uncertainty has been explained in § 6. The 

 value of m thus obtained would be the true value if the 

 assumed law were strictly correct and the value of A satisfying 

 the observations could be accurately obtained. But for reasons 

 already given different forms of expression, and different values 

 of the constants in the same expressions, giving rise to very 

 different absolute values of the functions, and of the value of 

 m, can be obtained which all satisfy observation almost equally 

 well. The value of m, therefore, thus obtained, can at best be 

 regarded merely as a rough approximation to the true value. 



8. By (4) we have for each value of d and corresponding ob- 

 served value of R, 



(14) A = 



and from (8) 



(15) A = 



q e — 1 



These quotients or values of A, for each value of d and R, 

 except so far as they are affected by errors of observation, 

 should be a constant if the assumed law is correct. We can 

 therefore test the assumed laws in this way as well as by 

 means of the residuals as is done in § 4. Thus Stefan gives 

 the following observed differences in the rates of cooling 

 between a naked and silvered cylindrical thermometer corres- 

 ponding to the values of d gi«ven in the first line below, the 

 temperature of the inclosure being 20°. 



a — 1 

 R 



6 100° 



120° 



140° 



160° 



180° 



200° 



Differences 2-19° 



2-96 



3-73 



4-66 



5-74 



7-11 



f 1-911 



1-977 



1-950 



1-947 



L-944 



1-972 



r. .. -. j 1-329 



Quotients ■{ ^o-. 



1-363 



1-343 



1-341 



1-345 



1-375 



1-766 



1-742 



1-729 



1-718 



1-722 



{ -900 



■917 



•897 



■891 



•887 



•907 



The quotients of the first and second lines are those given by 

 Stefan for the laws of Dulong and Petit and his own respec- 

 tively, the first being obtained from (14) by putting a = 

 1"007T, and the second from (15), or its equivalent, by putting 

 e=4. The near equality of these quotients was considered as 

 a confirmation of the approximate correctness of both laws, as 

 deduced from these data, within the range of temperature 

 used. But the quotients of the last two lines are obtained from 

 the same expressions by putting «=1'0082 in the former and e 

 =4-2 in the latter, and these last quotients satisfy the condition 

 of equality about as well as the former. This method of test- 



